Bit interleaver for low-density parity check codeword having length of 64800 and code rate of 4/15 and 4096-symbol mapping, and bit interleaving method using same

ABSTRACT

A bit interleaver, a bit-interleaved coded modulation (BICM) device and a bit interleaving method are disclosed herein. The bit interleaver includes a first memory, a processor, and a second memory. The first memory stores a low-density parity check (LDPC) codeword having a length of 64800 and a code rate of 4/15. The processor generates an interleaved codeword by interleaving the LDPC codeword on a bit group basis. The size of the bit group corresponds to a parallel factor of the LDPC codeword. The second memory provides the interleaved codeword to a modulator for 4096-symbol mapping.

CROSS-REFERENCE TO RELATED APPLICATIONS

This application claims the benefit of Korean Patent Application No.10-2015-0023416, filed Feb. 16, 2015, which is hereby incorporated byreference herein in its entirety.

BACKGROUND

1. Technical Field

The present disclosure relates generally to an interleaver and, moreparticularly, to a bit interleaver that is capable of distributing bursterrors occurring in a digital broadcast channel.

2. Description of the Related Art

Bit-Interleaved Coded Modulation (BICM) is bandwidth-efficienttransmission technology, and is implemented in such a manner that anerror-correction coder, a bit-by-bit interleaver and a high-ordermodulator are combined with one another.

BICM can provide excellent performance using a simple structure becauseit uses a low-density parity check (LDPC) coder or a Turbo coder as theerror-correction coder. Furthermore, BICM can provide high-levelflexibility because it can select modulation order and the length andcode rate of an error correction code in various forms. Due to theseadvantages, BICM has been used in broadcasting standards, such as DVB-T2and DVB-NGH, and has a strong possibility of being used in othernext-generation broadcasting systems.

However, in spite of those advantages, BICM suffers from the rapiddegradation of performance unless burst errors occurring in a channelare appropriately distributed via the bit-by-bit interleaver.Accordingly, the bit-by-bit interleaver used in BICM should be designedto be optimized for the modulation order or the length and code rate ofthe error correction code.

SUMMARY

At least one embodiment of the present invention is directed to theprovision of an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

At least one embodiment of the present invention is directed to theprovision of a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 4/15 and a modulatorperforming 4096-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

In accordance with an aspect of the present invention, there is provideda bit interleaver, including a first memory configured to store alow-density parity check (LDPC) codeword having a length of 64800 and acode rate of 4/15; a processor configured to generate an interleavedcodeword by interleaving the LDPC codeword on a bit group basis, thesize of the bit group corresponding to a parallel factor of the LDPCcodeword; and a second memory configured to provide the interleavedcodeword to a modulator for 4096-symbol mapping.

The 4096-symbol mapping may be NUC (Non-Uniform Constellation) symbolmapping corresponding to 4096 constellations (symbols).

The parallel factor may be 360, and each of the bit groups may include360 bits.

The LDPC codeword may be represented by (u₀, u₁, . . . u_(N) _(ldpc) ⁻¹)(where N_(ldpc), is 64800), and may be divided into 180 bit groups eachincluding 360 bits, as in the following equation:

X _(j) ={u _(k)|360×j≦k<360×(j+1), 0≦k<N _(ldcp)} for0≦j<N _(group)

where X_(j) is an j-th bit group, N_(Idpc) is 64800, and N_(group) is180.

The interleaving may be performed using the following equation usingpermutation order:

Y _(j) =x _(π(j))0≦j≦N _(group)

where X_(j) is the j-th bit group, Y_(j) is an interleaved j-th bitgroup, and π(j) is a permutation order for bit group-based interleaving(bit group-unit interleaving).

The permutation order may correspond to an interleaving sequencerepresented by the following equation:

interleaving  sequence = {91  52  36  30  35  6  121  29  150  47  163  2  89  39  65  157  64  122  101  40  84  69  90  129  10  9  15  162  21  171  43  44  132  158  104  4  72  169  177  103  76  28  78  53  1  151  161  88  148  42  160  109  100  126  138  108  38  25  3  112  17  124  155  172  134  86  119  94  145  178  68  26  130  140  115  152  139  37  22  102  14  118  11  98  154  61  146  164  107  131  159  63  93  7  79  5  137  165  59  77  55  80  117  13  173  144  85  153  66  106  49  34  48  41  143  142  27  136  18  111  175  123  147  114  19  125  166  149  113  46  31  141  120  57  74  8  20  96  170  128  97  16  60  110  156  45  82  105  62  99  23  92  32  50  73  56  167  95  24  168  33  116  75  127  81  67  179  174  70  12  58  87  176  0  51  135  83  133  54  71}

In accordance with another aspect of the present invention, there isprovided a bit interleaving method, including storing an LDPC codewordhaving a length of 64800 and a code rate of 4/15; generating aninterleaved codeword by interleaving the LDPC codeword on a bit groupbasis corresponding to the parallel factor of the LDPC codeword; andoutputting the interleaved codeword to a modulator for 4096-symbolmapping.

In accordance with still another aspect of the present invention, thereis provided a BICM device, including an error-correction coderconfigured to output an LDPC codeword having a length of 64800 and acode rate of 4/15; a bit interleaver configured to interleave the LDPCcodeword on a bit group basis corresponding to the parallel factor ofthe LDPC codeword and output the interleaved codeword; and a modulatorconfigured to perform 4096-symbol mapping on the interleaved codeword.

BRIEF DESCRIPTION OF THE DRAWINGS

The above and other objects, features and advantages of the presentinvention will be more clearly understood from the following detaileddescription taken in conjunction with the accompanying drawings, inwhich:

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention;

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention;

FIG. 3 is a diagram illustrating the structure of a parity check matrix(PCM) corresponding to an LDPC code to according to an embodiment of thepresent invention;

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800;

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200;

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence;

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention; and

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

DETAILED DESCRIPTION

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings. Repeated descriptions anddescriptions of well-known functions and configurations that have beendeemed to make the gist of the present invention unnecessarily obscurewill be omitted below. The embodiments of the present invention areintended to fully describe the present invention to persons havingordinary knowledge in the art to which the present invention pertains.Accordingly, the shapes, sizes, etc. of components in the drawings maybe exaggerated to make the description obvious.

Embodiments of the present invention will be described in detail belowwith reference to the accompanying drawings.

FIG. 1 is a block diagram illustrating a broadcast signal transmissionand reception system according to an embodiment of the presentinvention.

Referring to FIG. 1, it can be seen that a BICM device 10 and a BICMreception device 30 communicate with each other over a wireless channel20.

The BICM device 10 generates an n-bit codeword by encoding k informationbits 11 using an error-correction coder 13. In this case, theerror-correction coder 13 may be an LDPC coder or a Turbo coder.

The codeword is interleaved by a bit interleaver 14, and thus theinterleaved codeword is generated.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group). In this case, the error-correction coder 13 maybe an LDPC coder having a length of 64800 and a code rate of 4/15. Acodeword having a length of 64800 may be divided into a total of 180 bitgroups. Each of the bit groups may include 360 bits, i.e., the parallelfactor of an LDPC codeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

In this case, the bit interleaver 14 prevents the performance of errorcorrection code from being degraded by effectively distributing bursterrors occurring in a channel. In this case, the bit interleaver 14 maybe separately designed in accordance with the length and code rate ofthe error correction code and the modulation order.

The interleaved codeword is modulated by a modulator 15, and is thentransmitted via an antenna 17.

In this case, the modulator 15 may be based on a concept includingsymbol mapper (symbol mapping device). In this case, the modulator 15may be a symbol mapping device performing 4096-symbol mapping which mapscodes onto 4096 constellations (symbols).

In this case, the modulator 15 may be a uniform modulator, such as aquadrature amplitude modulation (QAM) modulator, or a non-uniformmodulator.

The modulator 15 may be a symbol mapping device performing NUC(Non-Uniform Constellation) symbol mapping which uses 4096constellations (symbols).

The signal transmitted via the wireless channel 20 is received via theantenna 31 of the BICM reception device 30, and, in the BICM receptiondevice 30, is subjected to a process reverse to the process in the BICMdevice 10. That is, the received data is demodulated by a demodulator33, is deinterleaved by a bit deinterleaver 34, and is then decoded byan error correction decoder 35, thereby finally restoring theinformation bits.

It will be apparent to those skilled in the art that the above-describedtransmission and reception processes have been described within aminimum range required for a description of the features of the presentinvention and various processes required for data transmission may beadded.

FIG. 2 is an operation flowchart illustrating a broadcast signaltransmission and reception method according to an embodiment of thepresent invention.

Referring to FIG. 2, in the broadcast signal transmission and receptionmethod according to this embodiment of the present invention, input bits(information bits) are subjected to error-correction coding at stepS210.

That is, at step S210, an n-bit codeword is generated by encoding kinformation bits using the error-correction coder.

In this case, step S210 may be performed as in an LDPC encoding method,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,an interleaved codeword is generated by interleaving the n-bit codewordon a bit group basis at step S220.

In this case, the n-bit codeword may be an LDPC codeword having a lengthof 64800 and a code rate of 4/15. The codeword having a length of 64800may be divided into a total of 180 bit groups. Each of the bit groupsmay include 360 bits corresponding to the parallel factors of an LDPCcodeword.

In this case, the interleaving may be performed on a bit group basis (bya unit of a bit group) in accordance with an interleaving sequence,which will be described later.

Furthermore, in the broadcast signal transmission and reception method,the encoded data is modulated at step S230.

That is, at step S230, the interleaved codeword is modulated using themodulator.

In this case, the modulator may be based on a concept including symbolmapper (symbol mapping device). In this case, the modulator may be asymbol mapping device performing 4096-symbol mapping which maps codesonto 4096 constellations (symbols).

In this case, the modulator may be a uniform modulator, such as a QAMmodulator, or a non-uniform modulator.

The modulator may be a symbol mapping device performing NUC (Non-UniformConstellation) symbol mapping which uses 4096 constellations (symbols).

Furthermore, in the broadcast signal transmission and reception method,the modulated data is transmitted at step S240.

That is, at step S240, the modulated codeword is transmitted over thewireless channel via the antenna.

Furthermore, in the broadcast signal transmission and reception method,the received data is demodulated at step S250.

That is, at step S250, the signal transmitted over the wireless channelis received via the antenna of the receiver, and the received data isdemodulated using the demodulator.

Furthermore, in the broadcast signal transmission and reception method,the demodulated data is deinterleaved at step S260. In this case, thedeinterleaving of step S260 may be reverse to the operation of stepS220.

Furthermore, in the broadcast signal transmission and reception method,the deinterleaved codeword is subjected to error correction decoding atstep S270.

That is, at step S270, the information bits are finally restored byperforming error correction decoding using the error correction decoderof the receiver.

In this case, step S270 corresponds to a process reverse to that of anLDPC encoding method, which will be described later.

An LDPC code is known as a code very close to the Shannon limit for anadditive white Gaussian noise (AWGN) channel, and has the advantages ofasymptotically excellent performance and parallelizable decodingcompared to a turbo code.

Generally, an LDPC code is defined by a low-density parity check matrix(PCM) that is randomly generated. However, a randomly generated LDPCcode requires a large amount of memory to store a PCM, and requires alot of time to access memory. In order to overcome these problems, aquasi-cyclic LDPC (QC-LDPC) code has been proposed. A QC-LDPC code thatis composed of a zero matrix or a circulant permutation matrix (CPM) isdefined by a PCM that is expressed by the following Equation 1:

$\begin{matrix}{{H = \begin{bmatrix}J^{a_{11}} & J^{a_{12}} & \ldots & J^{a_{1\; n}} \\J^{a_{21}} & J^{a_{22}} & \ldots & J^{a_{2\; n}} \\\vdots & \vdots & \ddots & \vdots \\J^{a_{m\; 1}} & J^{a_{m\; 2}} & \ldots & J^{a_{mn}}\end{bmatrix}},{{{for}\mspace{14mu} a_{ij}} \in \left\{ {0,1,\ldots \mspace{14mu},{L - 1},\infty} \right\}}} & (1)\end{matrix}$

In this equation, J is a CPM having a size of L×L, and is given as thefollowing Equation 2. In the following description, L may be 360.

$\begin{matrix}{J_{L \times L} = \begin{bmatrix}0 & 1 & 0 & \ldots & 0 \\0 & 0 & 1 & \ldots & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots \\0 & 0 & 0 & \ldots & 1 \\1 & 0 & 0 & \ldots & 0\end{bmatrix}} & (2)\end{matrix}$

Furthermore, J^(i) is obtained by shifting an L×L identity matrix I (J⁰)to the right i (0≦i<L) times, and J^(∞) is an L×L zero matrix.Accordingly, in the case of a QC-LDPC code, it is sufficient if onlyindex exponent i is stored in order to store J¹, and thus the amount ofmemory required to store a PCM is considerably reduced.

FIG. 3 is a diagram illustrating the structure of a PCM corresponding toan LDPC code to according to an embodiment of the present invention.

Referring to FIG. 3, the sizes of matrices A and C are g×K and(N−K−g)×(K+g), respectively, and are composed of an L×L zero matrix anda CPM, respectively. Furthermore, matrix Z is a zero matrix having asize of g×(N−K−g), matrix D is an identity matrix having a size of(N−K−g)×(N−K−g), and matrix B is a dual diagonal matrix having a size ofg×g. In this case, the matrix B may be a matrix in which all elementsexcept elements along a diagonal line and neighboring elements below thediagonal line are 0, and may be defined as the following Equation 3:

$\begin{matrix}{B_{g \times g} = \begin{bmatrix}I_{L \times L} & 0 & 0 & \ldots & 0 & 0 & 0 \\I_{L \times L} & I_{L \times L} & 0 & \ldots & 0 & 0 & 0 \\0 & I_{L \times L} & I_{L \times L} & \vdots & 0 & 0 & 0 \\\vdots & \vdots & \vdots & \ddots & \vdots & \vdots & \vdots \\0 & 0 & 0 & \ldots & I_{L \times L} & I_{L \times L} & 0 \\0 & 0 & 0 & \ldots & 0 & I_{L \times L} & I_{L \times L}\end{bmatrix}} & (3)\end{matrix}$

where I_(L×L) is an identity matrix having a size of L×L.

That is, the matrix B may be a bit-wise dual diagonal matrix, or may bea block-wise dual diagonal matrix having identity matrices as itsblocks, as indicated by Equation 3. The bit-wise dual diagonal matrix isdisclosed in detail in Korean Patent Application Publication No.2007-0058438, etc.

In particular, it will be apparent to those skilled in the art that whenthe matrix B is a bit-wise dual diagonal matrix, it is possible toperform conversion into a Quasi-cyclic form by applying row or columnpermutation to a PCM including the matrix B and having a structureillustrated in FIG. 3.

In this case, N is the length of a codeword, and K is the length ofinformation.

The present invention proposes a newly designed QC-LDPC code in whichthe code rate thereof is 4/15 and the length of a codeword is 64800, asillustrated in the following Table 1. That is, the present inventionproposes an LDPC code that is designed to receive information having alength of 17280 and generate an LDPC codeword having a length of 64800.

Table 1 illustrates the sizes of the matrices A, B, C, D and Z of theQC-LDPC code according to the present invention:

TABLE 1 Sizes Code rate Length A B C D Z 4/15 64800 1800 × 17280 1800 ×1800 45720 × 19080 45720 × 45720 1800 × 45720

The newly designed LDPC code may be represented in the form of asequence (progression), an equivalent relationship is establishedbetween the sequence and matrix (parity bit check matrix), and thesequence may be represented, as follows:

Sequence Table 1st row: 276 1754 1780 3597 8549 15196 26305 27003 3388337189 41042 41849 42356 2nd row: 730 873 927 9310 9867 17594 21969 2510625922 31167 35434 37742 45866 3rd row: 925 1202 1564 2575 2831 2951 519313096 18363 20592 33786 34090 40900 4th row: 973 1045 1071 8545 898011983 18649 21323 22789 22843 26821 36720 37856 5th row: 402 1038 16892466 2893 13474 15710 24137 29709 30451 35568 35966 46436 6th row: 263271 395 5089 5645 15488 16314 28778 29729 34350 34533 39608 45371 7throw: 387 1059 1306 1955 6990 20001 24606 28167 33802 35181 38481 3868845140 8th row: 53 851 1750 3493 11415 18882 20244 23411 28715 3072236487 38019 45416 9th row: 810 1044 1772 3906 5832 16793 17333 1791023946 29650 34190 40673 45828 10th row: 97 491 948 12156 13788 2497033774 37539 39750 39820 41195 46464 46820 11st row: 192 899 1283 37327310 13637 13810 19005 24227 26772 31273 37665 44005 12th row: 424 5311300 4860 8983 10137 16323 16888 17933 22458 26917 27835 37931 13th row:130 279 731 3024 6378 18838 19746 21007 22825 23109 28644 32048 3466714th row: 938 1041 1482 9589 10065 11535 17477 25816 27966 35022 3502542536 15th row: 170 454 1312 5326 6765 23408 24090 26072 33037 3808842985 46413 16th row: 220 804 843 2921 4841 7760 8303 11259 21058 2127634346 37604 17th row: 676 713 832 11937 12006 12309 16329 26438 3421437471 38179 42420 18th row: 714 931 1580 6837 9824 11257 15556 2673032053 34461 35889 45821 19th row: 28 1097 1340 8767 9406 17253 2955832857 37856 38593 41781 47101 20th row: 158 722 754 14489 23851 2816030371 30579 34963 44216 46462 47463 21st row: 833 1326 1332 7032 956611011 21424 26827 29789 31699 32876 37498 22nd row: 251 504 1075 44707736 11242 20397 32719 34453 36571 40344 46341 23rd row: 330 581 86815168 20265 26354 33624 35134 38609 44965 45209 46909 24th row: 729 16431732 3946 4912 9615 19699 30993 33658 38712 39424 46799 25th row: 546982 1274 9264 11017 11868 15674 16277 19204 28606 39063 43331 26th row:73 1160 1196 4334 12560 13583 14703 18270 18719 19327 38985 46779 27throw: 1147 1625 1759 3767 5912 11599 18561 19330 29619 33671 43346 4409828th row: 104 1507 1586 9387 17890 23532 27008 27861 30966 33579 3554139801 29th row: 1700 1746 1793 4941 7814 13746 20375 27441 30262 3039235385 42848 30th row: 183 555 1029 3090 5412 8148 19662 23312 2393328179 29962 35514 31st row: 891 908 1127 2827 4077 4376 4570 26923 2745633699 43431 46071 32nd row: 404 1110 1782 6003 14452 19247 26998 3013731404 31624 46621 47366 33rd row: 886 1627 1704 8193 8980 9648 1092816267 19774 35111 38545 44735 34th row: 268 380 1214 4797 5168 9109 928817992 21309 33210 36210 41429 35th row: 572 1121 1165 6944 7114 2097823540 25863 26190 26365 41521 44690 36th row: 18 185 496 5885 6165 2046823895 24745 31226 33680 37665 38587 37th row: 289 527 1118 11275 1201518088 22805 24679 28262 30160 34892 43212 38th row: 658 926 1589 763416231 22193 25320 26057 26512 27498 29472 34219 39th row: 337 801 15252023 3512 16031 26911 32719 35620 39035 43779 44316 40th row: 248 534670 6217 11430 24090 26509 28712 33073 33912 38048 39813 41st row: 821556 1575 7879 7892 14714 22404 22773 25531 34170 38203 38254 42nd row:247 313 1224 3694 14304 24033 26394 28101 37455 37859 38997 41344 43rdrow: 790 887 1418 2811 3288 9049 9704 13303 14262 38149 40109 40477 44throw: 1310 1384 1471 3716 8250 25371 26329 26997 30138 40842 41041 4492145th row: 86 288 367 1860 8713 18211 22628 22811 28342 28463 40415 4584546th row: 719 1438 1741 8258 10797 29270 29404 32096 34433 34616 3603045597 47th row: 215 1182 1364 8146 9949 10498 18603 19304 19803 2368543304 45121 48th row: 1243 1496 1537 8484 8851 16589 17665 20152 2428328993 34274 39795 49th row: 6320 6785 15841 16309 20512 25804 2742128941 43871 44647 50th row: 2207 2713 4450 12217 16506 21188 23933 2878938099 42392 51st row: 14064 14307 14599 14866 17540 18881 21065 2582330341 36963 52nd row: 14259 14396 17037 26769 29219 29319 31689 3301335631 37319 53rd row: 7798 10495 12868 14298 17221 23344 31908 3980941001 41965

An LDPC code that is represented in the form of a sequence is beingwidely used in the DVB standard.

According to an embodiment of the present invention, an LDPC codepresented in the form of a sequence is encoded, as follows. It isassumed that there is an information block S=(s₀, s₁, . . . , s_(K−1))having an information size K. The LDPC encoder generates a codewordΛ=(λ₀, λ₁, λ₂, . . . , λ_(N−1)) having a size of N=K+M₁+M₂ using theinformation block S having a size K. In this case, M₁=g, and M₂=N−K−g.Furthermore, M₁ is the size of parity bits corresponding to the dualdiagonal matrix B, and M₂ is the size of parity bits corresponding tothe identity matrix D. The encoding process is performed, as follows:

Initialization:

λ_(i) =s _(i) for i=0,1, . . . ,K−1

p _(j)=0 for j=0,1, . . . ,M ₁ +M ₂−1  (4)

First information bit λ₀ is accumulated at parity bit addressesspecified in the 1st row of the sequence of the Sequence Table. Forexample, in an LDPC code having a length of 64800 and a code rate of4/15, an accumulation process is as follows:

P₂₇₆=P₂₇₆⊕λ₀ P₁₇₅₄=P₁₇₅₄⊕λ₀ P₁₇₈₀=P₁₇₈₀⊕λ₀ P₃₅₉₇=P₃₅₉₇⊕λ₀ P₈₅₄₉=P₈₅₄₉⊕λ₀P₁₅₁₉₆=P₁₅₁₉₆⊕λ₀ P₂₆₃₀₅=P₂₆₃₀₅⊕λ₀ P₂₇₀₀₃=P₂₇₀₀₃ ⊕λ₀ P₃₃₈₈₃=P₃₃₈₈₃⊕λ₀P₃₇₁₈₉=P₃₇₁₈₉⊕λ₀ P₄₁₀₄₂=P₄₁₀₄₂⊕λ₀ P₄₁₈₄₉=P₄₁₈₄₉ ⊕λ₀ P₄₂₃₅₆=P₄₂₃₅₆⊕λ₀where the addition ⊕ occurs in GF(2).

The subsequent L−1 information bits, that is, λ_(m), m=1, 2, . . . ,L−1, are accumulated at parity bit addresses that are calculated by thefollowing Equation 5:

(x+m×Q ₁)mod M ₁ if x<M ₁

M ₁+{(x−M ₁ +m×Q ₂)mod M ₂} if x≧M ₁  (5)

where x denotes the addresses of parity bits corresponding to the firstinformation bit λ₀, that is, the addresses of the parity bits specifiedin the first row of the sequence of the Sequence Table, Q₁=M₁/L,Q₂=M₂/L, and L=360. Furthermore, Q₁ and Q₂ are defined in the followingTable 2. For example, for an LDPC code having a length of 64800 and acode rate of 4/15, M₁=1800, Q₁=5, M₂=45720, Q₂=127 and L=360, and thefollowing operations are performed on the second bit λ₁ using Equation5:P₂₈₁=P₂₈₁⊕λ₁ P₁₇₅₉=P₁₇₅₉⊕λ₁ P₁₇₈₅=P₁₇₈₅⊕λ₁ P₃₇₂₄=P₃₇₂₄⊕λ₁ P₈₆₇₆=P₈₆₇₆⊕λ₁P₁₅₃₂₃=P₁₅₃₂₃⊕λ₁ P₂₆₄₃₂=P₂₆₄₃₂⊕λ₁ P₂₇₁₃₀=P₂₇₁₃₀⊕λ₁ P₃₄₀₁₀=P₃₄₀₁₀⊕λ₁P₃₇₃₁₆=P₃₇₃₁₆⊕λ₁ P₄₁₁₆₉=P₄₁₁₆₉∥λ₁ P₄₁₉₇₆=P₄₁₉₇₆⊕λ₁ P₄₂₄₈₃=P₄₂₄₈₃⊕λ₁

Table 2 illustrates the sizes of M₁, Q₁, M₂ and Q₂ of the designedQC-LDPC code:

TABLE 2 Sizes Code rate Length M₁ M₂ Q₁ Q₂ 4/15 64800 1800 45720 5 127

The addresses of parity bit accumulators for new 360 information bitsfrom λ_(L) to λ_(2L−1) are calculated and accumulated from Equation 5using the second row of the sequence.

In a similar manner, for all groups composed of new L information bits,the addresses of parity bit accumulators are calculated and accumulatedfrom Equation 5 using new rows of the sequence.

After all the information bits from λ₀ to λ_(K−1) have been exhausted,the operations of the following Equation 6 are sequentially performedfrom i=1:

p _(i) =p _(i) ⊕p _(i−1) for i=0,1, . . . ,M ₁−1  (6)

Thereafter, when a parity interleaving operation, such as that of thefollowing Equation 7, is performed, parity bits corresponding to thedual diagonal matrix B are generated:

λ_(K+L·t+s) =p _(Q) ₁ _(·s+t) for 0≦s<L,0≦t<Q ₁  (7)

When the parity bits corresponding to the dual diagonal matrix B havebeen generated using K information bits λ₀, λ₁, . . . , λ_(K−1) paritybits corresponding to the identity matrix D are generated using the M₁generated parity bits λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹.

For all groups composed of L information bits from Δ_(K) to λ_(K+M) ₁⁻¹, the addresses of parity bit accumulators are calculated using thenew rows (starting with a row immediately subsequent to the last rowused when the parity bits corresponding to the dual diagonal matrix Bhave been generated) of the sequence and Equation 5, and relatedoperations are performed.

When a parity interleaving operation, such as that of the followingEquation 8, is performed after all the information bits from λ_(K) toλ_(K+M) ₁ ⁻¹ have been exhausted, parity bits corresponding to theidentity matrix D are generated:

λ_(K+M) ₁ _(+L·t+s) =p _(M) ₁ _(+Q) ₂ _(·s+t) for 0≦s<L,0≦t<Q ₂  (8)

FIG. 4 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 64800.

Referring to FIG. 4, it can be seen that an LDPC codeword having alength of 64800 is divided into 180 bit groups (a 0th group to a 179thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 64800is divided into 180 bit groups, as illustrated in FIG. 4, and each ofthe bit groups includes 360 bits.

FIG. 5 is a diagram illustrating the bit groups of an LDPC codewordhaving a length of 16200.

Referring to FIG. 5, it can be seen that an LDPC codeword having alength of 16200 is divided into 45 bit groups (a 0th group to a 44thgroup).

In this case, 360 may be the parallel factor (PF) of the LDPC codeword.That is, since the PF is 360, the LDPC codeword having a length of 16200is divided into 45 bit groups, as illustrated in FIG. 5, and each of thebit groups includes 360 bits.

FIG. 6 is a diagram illustrating interleaving that is performed on a bitgroup basis in accordance with an interleaving sequence.

Referring to FIG. 6, it can be seen that interleaving is performed bychanging the order of bit groups by a designed interleaving sequence.

For example, it is assumed that an interleaving sequence for an LDPCcodeword having a length of 16200 is as follows:

interleaving sequence={24 34 15 11 2 28 17 25 5 38 19 13 6 39 1 14 33 3729 12 42 31 30 32 36 40 26 35 44 4 16 8 20 43 21 7 0 18 23 3 10 41 9 2722}

Then, the order of the bit groups of the LDPC codeword illustrated inFIG. 4 is changed into that illustrated in FIG. 6 by the interleavingsequence.

That is, it can be seen that each of the LDPC codeword 610 and theinterleaved codeword 620 includes 45 bit groups, and it can be also seenthat, by the interleaving sequence, the 24th bit group of the LDPCcodeword 610 is changed into the 0th bit group of the interleaved LDPCcodeword 620, the 34th bit group of the LDPC codeword 610 is changedinto the 1st bit group of the interleaved LDPC codeword 620, the 15thbit group of the LDPC codeword 610 is changed into the 2nd bit group ofthe interleaved LDPC codeword 620, and the 11st bit group of the LDPCcodeword 610 is changed into the 3rd bit group of the interleaved LDPCcodeword 620, and the 2nd bit group of the LDPC codeword 610 is changedinto the 4th bit group of the interleaved LDPC codeword 620.

An LDPC codeword (u₀, u₁, . . . u_(N) _(ldpc) ⁻¹) having a length ofN_(ldpc) is divided into N_(group)=N_(ldpc)/360 bit groups, as inEquation 9 below:

X _(j) ={u _(k)|360×j≦k<360×(j+1),0≦k<N _(ldpc)} for 0≦j<N _(group)  (9)

where X_(j) is an j-th bit group, and each X_(j) is composed of 360bits.

The LDPC codeword divided into the bit groups is interleaved, as inEquation 10 below:

Y _(j) =X _(π(j))0≦j≦N _(group)  (10)

where Y_(j) is an interleaved j-th bit group, and π(j) is a permutationorder for bit group-based interleaving (bit group-unit interleaving).The permutation order corresponds to the interleaving sequence ofEquation 11 below:

$\begin{matrix}{{{interleaving}\mspace{14mu} {sequence}} = \left\{ {91\mspace{14mu} 52\mspace{14mu} 36\mspace{14mu} 30\mspace{14mu} 35\mspace{14mu} 6\mspace{14mu} 121\mspace{14mu} 29\mspace{14mu} 150\mspace{14mu} 47\mspace{14mu} 163\mspace{14mu} 2\mspace{14mu} 89\mspace{14mu} 39\mspace{14mu} 65\mspace{14mu} 157\mspace{14mu} 64\mspace{14mu} 122\mspace{14mu} 101\mspace{14mu} 40\mspace{14mu} 84\mspace{14mu} 69\mspace{14mu} 90\mspace{14mu} 129\mspace{14mu} 10\mspace{14mu} 9\mspace{14mu} 15\mspace{14mu} 162\mspace{14mu} 21\mspace{14mu} 171\mspace{14mu} 43\mspace{14mu} 44\mspace{14mu} 132\mspace{14mu} 158\mspace{14mu} 104\mspace{14mu} 4\mspace{14mu} 72\mspace{14mu} 169\mspace{14mu} 177\mspace{14mu} 103\mspace{14mu} 76\mspace{14mu} 28\mspace{14mu} 78\mspace{14mu} 53\mspace{14mu} 1\mspace{14mu} 151\mspace{14mu} 161\mspace{14mu} 88\mspace{14mu} 148\mspace{14mu} 42\mspace{14mu} 160\mspace{14mu} 109\mspace{14mu} 100\mspace{14mu} 126\mspace{14mu} 138\mspace{14mu} 108\mspace{14mu} 38\mspace{14mu} 25\mspace{14mu} 3\mspace{14mu} 112\mspace{14mu} 17\mspace{14mu} 124\mspace{14mu} 155\mspace{14mu} 172\mspace{14mu} 134\mspace{14mu} 86\mspace{14mu} 119\mspace{14mu} 94\mspace{14mu} 145\mspace{14mu} 178\mspace{14mu} 68\mspace{14mu} 26\mspace{14mu} 130\mspace{14mu} 140\mspace{14mu} 115\mspace{14mu} 152\mspace{14mu} 139\mspace{14mu} 37\mspace{14mu} 22\mspace{14mu} 102\mspace{14mu} 14\mspace{14mu} 118\mspace{14mu} 11\mspace{14mu} 98\mspace{14mu} 154\mspace{14mu} 61\mspace{14mu} 146\mspace{14mu} 164\mspace{14mu} 107\mspace{14mu} 131\mspace{14mu} 159\mspace{14mu} 63\mspace{14mu} 93\mspace{14mu} 7\mspace{14mu} 79\mspace{14mu} 5\mspace{14mu} 137\mspace{14mu} 165\mspace{14mu} 59\mspace{14mu} 77\mspace{14mu} 55\mspace{14mu} 80\mspace{14mu} 117\mspace{14mu} 13\mspace{14mu} 173\mspace{14mu} 144\mspace{14mu} 85\mspace{14mu} 153\mspace{14mu} 66\mspace{14mu} 106\mspace{14mu} 49\mspace{14mu} 34\mspace{14mu} 48\mspace{14mu} 41\mspace{14mu} 143\mspace{14mu} 142\mspace{14mu} 27\mspace{14mu} 136\mspace{14mu} 18\mspace{14mu} 111\mspace{14mu} 175\mspace{14mu} 123\mspace{14mu} 147\mspace{14mu} 114\mspace{14mu} 19\mspace{14mu} 125\mspace{14mu} 166\mspace{14mu} 149\mspace{14mu} 113\mspace{14mu} 46\mspace{14mu} 31\mspace{14mu} 141\mspace{14mu} 120\mspace{14mu} 57\mspace{14mu} 74\mspace{14mu} 8\mspace{14mu} 20\mspace{14mu} 96\mspace{14mu} 170\mspace{14mu} 128\mspace{14mu} 97\mspace{14mu} 16\mspace{14mu} 60\mspace{14mu} 110\mspace{14mu} 156\mspace{14mu} 45\mspace{14mu} 82\mspace{14mu} 105\mspace{14mu} 62\mspace{14mu} 99\mspace{14mu} 23\mspace{14mu} 92\mspace{14mu} 32\mspace{14mu} 50\mspace{14mu} 73\mspace{14mu} 56\mspace{14mu} 167\mspace{14mu} 95\mspace{14mu} 24\mspace{14mu} 168\mspace{14mu} 33\mspace{14mu} 116\mspace{14mu} 75\mspace{14mu} 127\mspace{14mu} 81\mspace{14mu} 67\mspace{14mu} 179\mspace{14mu} 174\mspace{14mu} 70\mspace{14mu} 12\mspace{14mu} 58\mspace{14mu} 87\mspace{14mu} 176\mspace{14mu} 0\mspace{14mu} 51\mspace{14mu} 135\mspace{14mu} 83\mspace{14mu} 133\mspace{14mu} 54\mspace{14mu} 71} \right\}} & (11)\end{matrix}$

That is, when each of the codeword and the interleaved codeword includes180 bit groups ranging from a 0th bit group to a 179th bit group, theinterleaving sequence of Equation 11 means that the 91st bit group ofthe codeword becomes the 0th bit group of the interleaved codeword, the52nd bit group of the codeword becomes the 1st bit group of theinterleaved codeword, the 36th bit group of the codeword becomes the 2ndbit group of the interleaved codeword, the 30th bit group of thecodeword becomes the 3rd bit group of the interleaved codeword, . . . ,the 54th bit group of the codeword becomes the 178th bit group of theinterleaved codeword, and the 71st bit group of the codeword becomes the179th bit group of the interleaved codeword.

In particular, the interleaving sequence of Equation 11 has beenoptimized for a case where 4096-symbol mapping (NUC symbol mapping) isemployed and an LDPC coder having a length of 64800 and a code rate of4/15 is used.

FIG. 7 is a block diagram illustrating a bit interleaver according to anembodiment of the present invention.

Referring to FIG. 7, the bit interleaver according to the presentembodiment includes memories 710 and 730 and a processor 720.

The memory 710 stores an LDPC codeword having a length of 64800 and acode rate of 4/15.

The processor 720 generates an interleaved codeword by interleaving theLDPC codeword on a bit group basis corresponding to the parallel factorof the LDPC codeword.

In this case, the parallel factor may be 360. In this case, each of thebit groups may include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

The memory 730 provides the interleaved codeword to a modulator for4096-symbol mapping.

In this case, the modulator may be a symbol mapping device performingNUC (Non-Uniform Constellation) symbol mapping.

The memories 710 and 730 may correspond to various types of hardware forstoring a set of bits, and may correspond to a data structure, such asan array, a list, a stack, a queue or the like.

In this case, the memories 710 and 730 may not be physically separatedevices, but may correspond to different addresses of a physicallysingle device. That is, the memories 710 and 730 are not physicallydistinguished from each other, but are merely logically distinguishedfrom each other.

The error-correction coder 13 illustrated in FIG. 1 may be implementedin the same structure as in FIG. 7.

That is, the error-correction coder may include memories and aprocessor. In this case, the first memory is a memory that stores anLDPC codeword having a length of 64800 and a code rate of 4/15, and asecond memory is a memory that is initialized to 0.

The memories may correspond to λ_(i)(i=0, 1, . . . , N−1) and P_(j)(j=0,1, . . . , M₁+M₂−1), respectively.

The processor may generate an LDPC codeword corresponding to informationbits by performing accumulation with respect to the memory using asequence corresponding to a parity check matrix (PCM).

In this case, the accumulation may be performed at parity bit addressesthat are updated using the sequence of the above Sequence Table.

In this case, the LDPC codeword may include a systematic part λ₀, λ₁, .. . , λ_(K−1) corresponding to the information bits and having a lengthof 17280 (=K), a first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹corresponding to a dual diagonal matrix included in the PCM and having alength of 1800 (=M₁=g), and a second parity part λ_(K+M) ₁ , λ_(K+M) ₁₊₁, . . . , λ_(K+M) ₁ _(+M) ₂ ⁻¹ corresponding to an identity matrixincluded in the PCM and having a length of 45720 (=M₂).

In this case, the sequence may have a number of rows equal to the sum(17280/360+1800/360=53) of a value obtained by dividing the length ofthe systematic part, i.e., 17280, by a CPM size L corresponding to thePCM, i.e., 360, and a value obtained by dividing the length M₁ of thefirst parity part, i.e., 1800, by 360.

As described above, the sequence may be represented by the aboveSequence Table.

In this case, the second memory may have a size corresponding to the sumM₁+M₂ of the length M₁ of the first parity part and the length M₂ of thesecond parity part.

In this case, the parity bit addresses may be updated based on theresults of comparing each x of the previous parity bit addresses,specified in respective rows of the sequence, with the length M₁ of thefirst parity part.

That is, the parity bit addresses may be updated using Equation 5. Inthis case, x may be the previous parity bit addresses, m may be aninformation bit index that is an integer larger than 0 and smaller thanL, L may be the CPM size of the PCM, Q₁ may be M₁/L, M₁ may be the sizeof the first parity part, Q₂ may be M₂/L, and M₂ may be the size of thesecond parity part.

In this case, it may be possible to perform the accumulation whilerepeatedly changing the rows of the sequence by the CPM size L (=360) ofthe PCM, as described above.

In this case, the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹may be generated by performing parity interleaving using the firstmemory and the second memory, as described in conjunction with Equation7.

In this case, the second parity part λ_(K+M) ₁ , λ_(K+M) ₁ ₊₁, . . .λ_(K+M) ₁ _(+M) ₂ ⁻¹ may be generated by performing parity interleavingusing the first memory and the second memory after generating the firstparity part λ_(K), λ_(K+1), . . . , λ_(K+M) ₁ ⁻¹ and then performing theaccumulation using the first parity part λ_(K), λ_(K+1), . . . , λ_(K+M)₁ ⁻¹ and the sequence, as described in conjunction with Equation 8.

FIG. 8 is an operation flowchart illustrating a bit interleaving methodaccording to an embodiment of the present invention.

Referring to FIG. 8, in the bit interleaving method according to thepresent embodiment, an LDPC codeword having a length of 64800 and a coderate of 4/15 is stored at step S810.

In this case, the LDPC codeword may be represented by (u₀, u₁, . . . ,u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and may be divided into 180bit groups each composed of 360 bits, as in Equation 9.

Furthermore, in the bit interleaving method according to the presentembodiment, an interleaved codeword is generated by interleaving theLDPC codeword on a bit group basis at step S820.

In this case, the size of the bit group may correspond to the parallelfactor of the LDPC codeword.

In this case, the interleaving may be performed using Equation 10 usingpermutation order.

In this case, the permutation order may correspond to the interleavingsequence represented by Equation 11.

In this case, the parallel factor may be 360, and each of the bit groupsmay include 360 bits.

In this case, the LDPC codeword may be divided into 180 bit groups, asin Equation 9.

Moreover, in the bit interleaving method according to the presentembodiment, the interleaved codeword is output to a modulator for4096-symbol mapping at step 830.

In accordance with at least one embodiment of the present invention,there is provided an intra-BICM bit interleaver that can effectivelydistribute burst errors occurring in a broadcasting system channel.

In accordance with at least one embodiment of the present invention,there is provided a bit interleaver that is optimized for an LDPC coderhaving a length of 64800 and a code rate of 4/15 and a modulatorperforming 4096-symbol mapping and, thus, can be applied tonext-generation broadcasting systems, such as ATSC 3.0.

Although the specific embodiments of the present invention have beendisclosed for illustrative purposes, those skilled in the art willappreciate that various modifications, additions and substitutions arepossible without departing from the scope and spirit of the invention asdisclosed in the accompanying claims.

What is claimed is:
 1. A bit interleaver, comprising: a first memoryconfigured to store a low-density parity check (LDPC) codeword having alength of 64800 and a code rate of 4/15; a processor configured togenerate an interleaved codeword by interleaving the LDPC codeword on abit group basis, the size of the bit group corresponding to a parallelfactor of the LDPC codeword; and a second memory configured to providethe interleaved codeword to a modulator for 4096-symbol mapping.
 2. Thebit interleaver of claim 1, wherein the 4096-symbol mapping is aNon-Uniform Constellation (NUC) symbol mapping which corresponds to 4096constellations.
 3. The bit interleaver of claim 2, wherein the parallelfactor is 360, and the bit group includes 360 bits.
 4. The bitinterleaver of claim 3, wherein the LDPC codeword is represented by (u₀,u₁, . . . , u_(N) _(ldpc) ⁻¹) (where N_(ldpc) is 64800), and is dividedinto 180 bit groups each including 360 bits, as in the followingequation:X _(j) ={u _(k)|360×j≦k<360×(j+1),0≦k<N _(ldpc)} for 0≦j<N _(group)where X_(j) is an j-th bit group, N_(ldpc) is 64800, and N_(group) is180.
 5. The bit interleaver of claim 4, wherein the interleaving isperformed using the following equation using permutation order:Y _(j) =X _(π(j))0≦j≦N _(group) where X_(j) is the j-th bit group, Y_(j)is an interleaved j-th bit group, and π(j) is a permutation order forbit group-based interleaving.
 6. The bit interleaver of claim 5, whereinthe permutation order corresponds to an interleaving sequencerepresented by the following equation:interleaving  sequence = {91  52  36  30  35  6  121  29  150  47  163  2  89  39  65  157  64  122  101  40  84  69  90  129  10  9  15  162  21  171  43  44  132  158  104  4  72  169  177  103  76  28  78  53  1  151  161  88  148  42  160  109  100  126  138  108  38  25  3  112  17  124  155  172  134  86  119  94  145  178  68  26  130  140  115  152  139  37  22  102  14  118  11  98  154  61  146  164  107  131  159  63  93  7  79  5  137  165  59  77  55  80  117  13  173  144  85  153  66  106  49  34  48  41  143  142  27  136  18  111  175  123  147  114  19  125  166  149  113  46  31  141  120  57  74  8  20  96  170  128  97  16  60  110  156  45  82  105  62  99  23  92  32  50  73  56  167  95  24  168  33  116  75  127  81  67  179  174  70  12  58  87  176  0  51  135  83  133  54  71}